Average Error: 53.0 → 5.8
Time: 15.7s
Precision: 64
\[4.930380657631324 \cdot 10^{-32} \lt a \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt b \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt c \lt 2.028240960365167 \cdot 10^{+31}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\frac{c}{b} \cdot \frac{-1}{2}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}
↓
\frac{c}{b} \cdot \frac{-1}{2}
double f(double a, double b, double c) {
        double r3628976 = b;
        double r3628977 = -r3628976;
        double r3628978 = r3628976 * r3628976;
        double r3628979 = 3.0;
        double r3628980 = a;
        double r3628981 = r3628979 * r3628980;
        double r3628982 = c;
        double r3628983 = r3628981 * r3628982;
        double r3628984 = r3628978 - r3628983;
        double r3628985 = sqrt(r3628984);
        double r3628986 = r3628977 + r3628985;
        double r3628987 = r3628986 / r3628981;
        return r3628987;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r3628988 = c;
        double r3628989 = b;
        double r3628990 = r3628988 / r3628989;
        double r3628991 = -0.5;
        double r3628992 = r3628990 * r3628991;
        return r3628992;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 53.0

    \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]

  2. Simplified53.0

    \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c} - b}{3 \cdot a}}\]

  3. Taylor expanded around inf 5.8

    \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{c}{b}}\]

  4. Final simplification5.8

    \[\leadsto \frac{c}{b} \cdot \frac{-1}{2}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (a b c)
  :name "Cubic critical, wide range"
  :pre (and (< 4.930380657631324e-32 a 2.028240960365167e+31) (< 4.930380657631324e-32 b 2.028240960365167e+31) (< 4.930380657631324e-32 c 2.028240960365167e+31))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a)))